Quantum local asymptotic normality based on a new quantum likelihood ratio

TL;DR

This paper introduces a new quantum local asymptotic normality framework using a novel quantum likelihood ratio, enabling the proof of the Holevo bound's achievability for local shift parameters in quantum statistics.

Contribution

It develops a quantum local asymptotic normality theory based on a new quantum likelihood ratio applicable to smooth quantum models.

Findings

Proves the asymptotic achievability of the Holevo bound.

Establishes a quantum analogue of the classical log-likelihood ratio.

Applicable to a broad class of quantum statistical models.

Abstract

We develop a theory of local asymptotic normality in the quantum domain based on a novel quantum analogue of the log-likelihood ratio. This formulation is applicable to any quantum statistical model satisfying a mild smoothness condition. As an application, we prove the asymptotic achievability of the Holevo bound for the local shift parameter.